Quote:
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Originally Posted by Jimro
…the longer the acceleration the lower the peak energy delivered over the recoil impulse.
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Peak energy is the same as final energy for the gun. It depends on the square of the final velocity of the gun, not the bullet. The gun's mass is not changed when you change the weight of the bullet, so the longer it experiences acceleration at a given level of force, the faster it goes and the more kinetic energy it has.
Quote:
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Originally Posted by Jimro
So the LONGER a bullet spends in the barrel the LESS momentum you'll get.
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Only if you don't change the mass of the bullet, as we did in the example.
To simplify considerations, assume you adjust powder choice and charge weight so the pressure profiles are the same with respect to distance down the bore for the light bullet and the heavy bullet. In other words, the pressure at the bullet base at any bullet distance along the barrel is the same for both the light and heavy bullet examples.
a=
F/
m, so that as the mass of the bullet gets bigger the
bullet's acceleration gets smaller, but the equal and opposite force is the same and the gun's mass is the same, so the
gun's acceleration is
not smaller. The gun's acceleration is just as big but now lasts longer because the heavier bullet takes longer to clear the tube. The result is the gun has more velocity, and, with the square of that, more energy at the end of the firing event.
All this is spelled out in the SAAMI document I linked to in post #7. I recommend downloading a copy and working a few examples to satisfy yourself that it's true.